Arrive at the exact ratio of these sums

This article is in continuation to the last article focusing on the ratio and proportion topic. Here are some practice questions along with solutions that will help you in your preparation for the State government recruitment tests. 1. Two numbers are in the ratio 5 : 7. If 9 is subtracted from each of them, […]

This article is in continuation to the last article focusing on the ratio and proportion topic. Here are some practice questions along with solutions that will help you in your preparation for the State government recruitment tests.

1. Two numbers are in the ratio 5 : 7. If 9 is subtracted from each of them, their ratio becomes 7 : 11. The difference of the numbers is?

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a) 14 b) 10 c) 12 d) 15

Ans: c

Solution: Let the numbers be 5x and 7x.
Now,
(5x – 9)/ (7x – 9) = 7/11
=>; 11 (5x – 9) = 7 (7x – 9)
=>; 55x – 99 = 49x – 63
=>; 55x – 49x = 99 – 63
=>; 6x = 36
=>; x = 6
 Required difference
= 7x – 5x = 2x = 2 × 6 = 12

2. Two numbers are in the ratio 1 1/2: 2 2/3 . When each of these is increased by 15, they become in the ratio 1 2/3 : 2 1/2 . The greater of the numbers is?

a) 22 b) 30 c) 48 d) 52

Ans: c

Solution: Let the numbers be 3/2 x and 8/3 x
According to question,
(3/2 x 15) / (8x/3 15) = (5/3) / (5/2)
=>; {(3x 30) / 2} / {(8x 45) / 3} = 2/3
3 (3x 30) / 2 (8x 45) = 2/3
(9x 90) / (16x 90) = 2/3
27x 270 = 32x 180
32x – 27x = 270 – 180 = 90
5x = 90 x = 18
 The greater number
= 8/3 x = 8/3 × 18 = 48

3. Two numbers are in the ratio 3 : 5. If 9 is subtracted from each, then they are in the ratio 12 : 23. Find the smaller number.

a) 33 b) 22 c) 44 d) 66

Ans: a

Solution: Let the numbers be 3x and 5x.
 (3x – 9) / (5x – 9) = 12/23
=>; 69x – 60x = 207 – 108
=>; x = 99/9 = 11
 The smaller number
= 3x = 33

4. Students in three classes are in the ratio 2 : 3 : 5. If 20 students are increased in each class, the ratio changes to 4 : 5 : 7. Originally the total number of students was?

a) 150 b) 100 c) 80 d) 250

Ans: b

Solution: Let the original number of students in three classes be 2x, 3x and 5x respectively.
As given,
(2x 20) / (3x 20) = 4/5
=>; 10x 100 = 12x 80
=>; 12x – 10x = 100 – 80
=>; 2x = 20
=>; x = 20/2 = 10
 Total number of students originally
= 2x 3x 5x = 10x
= 10 × 10 = 100

5. The ratio of the number of boys and that of girls in a school having 504 students is 13 :11. What will be the new ratio if 3 more girls are admitted?

a) 13 : 14 b) 6 : 7 c) 14 : 13 d) 7 : 6

Ans: d

Solution: Number of boys
13/(13 11) × 504
13/24 × 504 = 273
Number of girls
= 504 – 273 = 231
3 girls are admitted.
 Required ratio = 273 : 234
= 7 : 6

To be continued…